Title

Eigenvalue Problems for Exponential-Type Kernels

Published In

Computational Methods in Applied Mathematics

Document Type

Citation

Publication Date

1-1-2020

Abstract

We study approximations of eigenvalue problems for integral operators associated with kernel functions of exponential type. We show convergence rate |λk − λk,h| ≤ Ckh 2 in the case of lowest order approximation for both Galerkin and Nyström methods, where h is the mesh size, λk and λk,h are the exact and approximate kth largest eigenvalues, respectively. We prove that the two methods are numerically equivalent in the sense that |λk,h(G)k,h(N)| ≤ Ch2, where λk,h(G) and λk,h(N) denote the kth largest eigenvalues computed by Galerkin and Nyström methods, respectively, and C is a eigenvalue independent constant. The theoretical results are accompanied by a series of numerical experiments

Description

Copyright © 2011–2020 by Walter de Gruyter GmbH

DOI

10.1515/cmam-2018-0186

Persistent Identifier

https://archives.pdx.edu/ds/psu/32519

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